A339615 - OEIS

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A339615

Number of nonempty sets of distinct positive integers whose sum of cubes is a cube, the largest integer of a set is n.

1, 1, 1, 1, 2, 1, 1, 3, 1, 6, 5, 9, 10, 25, 32, 51, 97, 144, 244, 463, 767, 1062, 2005, 4177, 5716, 12101, 21526, 35306, 64629, 114871, 205337, 372317, 718410, 1226320, 2361112, 4308192, 7301384, 14615750, 26382095, 47631200, 91388286, 171931627, 302867194, 578843590, 1112232587

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

a(13) = 10 sets: {13}, {2, 3, 8, 13}, {4, 8, 11, 12, 13}, {1, 2, 6, 7, 11, 13}, {2, 5, 7, 8, 12, 13}, {3, 4, 8, 10, 11, 12, 13}, {1, 2, 3, 4, 5, 7, 11, 13}, {2, 3, 4, 6, 7, 8, 9, 13}, {1, 2, 5, 6, 7, 8, 9, 10, 12, 13} and {2, 3, 5, 7, 8, 9, 10, 11, 12, 13}.

PROG

(Python)

from functools import lru_cache

def perf_cube(n): return round(n**(1/3))**3 ==n

@lru_cache(maxsize=None)

def b(n, soc, c):

if n == 0:

if perf_cube(soc): return 1

return 0

return b(n-1, soc, c) + b(n-1, soc+n*n*n, c+1)

a = lambda n: b(n-1, n*n*n, 1)

print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Dec 10 2020